ASTRO 101

1. ASTRO 101 Principles of Astronomy

2. Instructor: Jerome A. Orosz (rhymes with “boris”)Contact: • Telephone: 594-7118 • E-mail: orosz@sciences.sdsu.edu • WWW: http://mintaka.sdsu.edu/faculty/orosz/web/ • Office: Physics 241, hours T TH 3:30-5:00

4. Homework/Announcements • Chapter 9 homework due April 23: Question 13 (Draw an H-R Diagram …)

5. Stellar Properties • The Sun and the stars are similar objects. • In order to understand them, we want to try and measure as many properties about them as we can: • Power output (luminosity) Measure distance and flux • Temperature at the “surface”color or spectral type • Radius • Mass • Chemical composition

6. Next: • Temperature-Luminosity diagrams • Binary stars

7. Temperature-Luminosity Diagrams • When you have a large number of objects, each with several observed characteristics, look for correlations between the observed properties. • Henry Norris Russell and Ejnar Hertzsprung were the first to do this with stars in the early 1900s. • Some measure of the temperature is plotted on the x-axis of the plot, and some measure of the intrinsic luminosity is plotted on the y-axis.

8. Temperature-Luminosity Diagrams • The stars do not fall on random locations in this diagram!

9. Temperature-Luminosity Diagrams • The stars do not fall on random locations in this diagram! • What does this mean? • This diagram gives us clues to inner workings of stars, and how they evolve. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

10. Temperature-Luminosity Diagrams • The stars do not fall on random locations in this diagram! • There is some specific physical process that limits where a star can be on this diagram. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

11. Temperature-Luminosity Diagrams • The stars do not fall on random locations in this diagram! • Furthermore, the location of a star on this diagram is an indicator of its size. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

12. Black Body Radiation • The luminosity, radius, and temperature of a black body are related: measure any two values, you can compute the third one. • Since stars are approximately black bodies, their location in the CMD indicates their radii.

13. Temperature-Luminosity Diagrams • Lines of constant radius go something like this: • Cool and luminous stars: large radii. • Hot and faint stars: small radii. • Most stars are here, and there is not a large variation in radius. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

14. Temperature-Luminosity Diagrams • This diagram shows some well-known stars. Most of the bright stars you see without a telescope are giants.

15. Temperature-Luminosity Diagrams • So far, we have found out that: • Stars occupy specific regions of the temperature-luminosity or color-magnitude diagram. • The inferred radii of stars spans a very wide range from “white dwarfs” with sizes similar to the Earth to “supergiants” with sizes equal to the Sun-Mars distance. • This is related to the life cycles of stars. But first, we must discuss binary stars and stellar “populations”…

16. Next:Other Stellar PropertiesBinary Stars

17. Stellar Properties • The Sun and the stars are similar objects. • In order to understand them, we want to try and measure as many properties about them as we can: • Temperature at the “surface” ---use spectral types • Power output (luminosity) --- flux and distance • Radius • Mass • Chemical composition

18. Other Stellar Properties • We can measure the temperature of a star relatively easily by its spectral type or color. If the distance is known, then we can measure its luminosity, and then compute its radius. Note, however, that the radius measured this way is not very accurate, owing to the uncertainty in the distance. • Is it possible to measure the radius of a distant star accurately? Also, are there other properties we can measure? Yes, use binary stars!

19. Detour: The Two-Body Problem • Use Newton’s Laws to describe the behavior of two objects under the influence of their mutual gravity. • We will apply it to binary star systems (e.g. a system consisting of two stars).

20. Center of Mass • For two point masses, the center of mass is along the line joining the two masses. • The center of mass is closer to the more massive body.

21. Center of Mass • Why is this useful? Two bodies acting under their mutual gravity will orbit in a plane about their center of mass. • Here is the case for equal masses.

22. Center of Mass • Why is this useful? Two bodies acting under their mutual gravity will orbit in a plane about their center of mass. • Here is the case for M1 = 2M2.

23. Binary Stars • A binary system is when two stars are bound together by gravity. They orbit their common center of mass. • In some cases, you can see two stars move around each other on the sky.

24. Binary Stars • A binary system is when two stars are bound together by gravity. They orbit their common center of mass. • In some cases, you can see two stars move around each other on the sky. • These are “visual binaries.”

25. Binary Stars

26. Binary Stars • A binary system is when two stars are bound together by gravity. They orbit their common center of mass. • In a visual binary, you can see two stars. • However, for most binary stars, their separation is very small compared to their distance, and from Earth they appear to be a single point. • How do you observe these types of binaries? Use spectroscopy!

27. Viewing Angle • The plane of the orbit is two dimensional, so depending on how that plane is tilted with respect to your line of sight you can see different things.

28. Detecting the Wobble • In Astronomy, any motion can be broken down into two groups: • Motion in the plane of the sky (e.g. east-west and north-south motion). • Motion towards or away from us (e.g. “radial velocities”). • Motions in the plane of the sky are usually small, and typically one has to wait many years to see a relatively big shift.

29. Detecting the Wobble • In Astronomy, any motion can be broken down into two groups: • Motion in the plane of the sky (e.g. east-west and north-south motion). • Motion towards or away from us (e.g. “radial velocities”). • Motions in the plane of the sky are usually small, and typically one has to wait many years to see a relatively big shift. One can see Sirius wobble over the course of decades (it has a very massive, but dark, companion).

30. Detecting the Wobble • In Astronomy, any motion can be broken down into two groups: • Motion in the plane of the sky (e.g. east-west and north-south motion). • Motion towards or away from us (e.g. “radial velocities”). • Motions in the plane of the sky are usually small, and typically one has to wait many years to see a relatively big shift. We can’t detect this motion in most binaries.

31. Detecting the Wobble • In Astronomy, any motion can be broken down into two groups: • Motion in the plane of the sky (e.g. east-west and north-south motion). • Motion towards or away from us (e.g. “radial velocities”). • Motions in the plane of the sky are usually small, and typically one has to wait many years to see a relatively big shift. We can’t detect this motion in most binaries.

32. Detecting Radial Velocities • Recall that radial velocities can be measured from Doppler shifts in the spectral lines:

33. Detecting Radial Velocities • Recall that radial velocities can be measured from Doppler shifts in the spectral lines: Motion towards us gives a shorter observed wavelength.

34. Detecting Radial Velocities • Recall that radial velocities can be measured from Doppler shifts in the spectral lines: Motion towards us gives a shorter observed wavelength. Motion away from us gives a longer observed wavelength.

35. Spectroscopic Binaries • Recall that radial velocities can be measured from Doppler shifts in the spectral lines: • Here are two spectra of Castor B, taken at two different times. The shift in the lines due to a change in the radial velocity is apparent.

36. Spectroscopic Binaries • The radial velocity of each star changes smoothly as the stars orbit each other. • These changes in the radial velocity can be measured using high resolution spectra.

37. Spectroscopic Binaries • Recall from that radial velocities can be measured from Doppler shifts in the spectral lines: Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

38. Spectroscopic Binaries • In some cases, you can see both stars in the spectrum. • In most cases, you can only see one star changing its radial velocity in a periodic way.

39. Binary Stars • A binary system is when two stars are bound together by gravity. They orbit their common center of mass. • In some cases, we can use binary stars to measure precise masses and radii for stars.

40. Center of Mass • Recall that m1r1=m2r2 • Also, note that velocity of the star is proportional to the distance to the center of mass since a star further from the COM has a greater distance to cover in the same amount of time. This implies m1v1=m2v2, or m1/m2=v2/v1 • The ratio of the velocities in inversely proportional to the mass ratio. Also, the same is true for radial velocities.

41. Center of Mass • If you can see both stars in the spectrum, then you may be able to use Doppler shifts to measure the radial velocities of both stars. This gives you the mass ratio, regardless of the viewing angle (e.g. nearly face-on, nearly edge-on, etc.).

42. Stellar Masses • If you can see both stars in the spectrum, then you may be able to use Doppler shifts to measure the radial velocities of both stars. This gives you the mass ratio, regardless of the viewing angle (e.g. nearly face-on, nearly edge-on, etc.). This is usually useful information. • If you can find the viewing angle, then you can compute true orbital velocities and use Kepler’s Laws and Newton’s theory to find the actual masses.

43. Viewing Angle • The plane of the orbit is two dimensional, so depending on how that plane is tilted with respect to your line of sight you can see different things.

44. Stellar Masses • If you can see both stars in the spectrum, then you may be able to use Doppler shifts to measure the radial velocities of both stars. This gives you the mass ratio, regardless of the viewing angle (e.g. nearly face-on, nearly edge-on, etc.). This is usually useful information. • If you can find the viewing angle, then you can compute true orbital velocities and use Kepler’s Laws and Newton’s theory to find the actual masses. How do you find the viewing angle?

45. Stellar Masses • If you can see both stars in the spectrum, then you may be able to use Doppler shifts to measure the radial velocities of both stars. This gives you the mass ratio, regardless of the viewing angle (e.g. nearly face-on, nearly edge-on, etc.). This is usually useful information. • If you can find the viewing angle, then you can compute true orbital velocities and use Kepler’s Laws and Newton’s theory to find the actual masses. Find eclipsing systems!

46. Definition • An eclipse, occultation, and transit essentially mean the same thing: one body passes in front of another as seen from earth.

47. Eclipsing Systems and Stellar Radii • Eclipsing systems must be nearly edge-on, since the stars appear to pass in front of each other as seen from Earth.

48. Eclipsing Systems and Stellar Radii • The relative radii can be found by studying how much light is blocked, and for how long. Image from Nick Strobel’s Astronomy Notes (http://www.astronomynotes.com)

49. Eclipsing Systems and Stellar Radii • The “light curve depends on the relative sizes and brightnesses of the stars, and on the orientation.

50. Eclipsing Systems and Stellar Radii • The “light curve depends on the relative sizes and brightnesses of the stars, and on the orientation. • Algol was known to be variable for a long time, and its periodic nature was established in 1783.